Three-dimensional strength criterion for rocks: A review

Deep rocks are typically under a true-triaxial stress state. The strength of deep rock is thus dictated by both the direction and magnitude of principal stresses. The formulation of three-dimensional strength criterion for rocks is thus essential for evaluating the stability of deep-buried rock structures. With advancements in true-triaxial experimental instrumentation, several three-dimensional strength criteria have been proposed, necessitating a systematic review and consolidation of these criteria. This review first introduces the concept of three-dimensional stress state. Subsequently, classical strength criteria such as the Mohr-Coulomb Criterion, the Hoek-Brown criterion, and the Drucker-Prager criterion are reiterated. However, these traditional strength criteria inadequately describe rock strength under true-triaxial stress conditions. To better capture the influence of intermediate principal stress, hydrostatic pressure, and Lode angle on rock strength, researchers have revised classical strength criteria. Modified strength criteria and unified strength criteria based on classical formulations are also introduced. Notably, the unified strength criterion incorporates multiple single criteria and demonstrates wider applicability. Furthermore, beyond macroscopic strength criteria, this review also discusses micromechanical strength criteria, where the stress state and crack propagation govern rock mechanical behaviors. This comprehensive review may serve as a valuable source for addressing the problem of deep rock strength in energy extraction and other rock engineering applications.